Advanced Placement Calculus AB covering limits, derivatives, and integrals.
Calculus gives us several shortcut rules for finding derivatives faster than using the definition every time.
For any real number \( n \):
\[ \frac{d}{dx}x^n = nx^{n-1} \]
For two functions \( f(x) \) and \( g(x) \):
\[ (fg)' = f'g + fg' \]
For composite functions \( f(g(x)) \):
\[ \frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x) \]
Many problems require combining these rules. Practice recognizing which rule to use and when!
\[f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\]
Given \( f(x) = x^3 \sin(x) \), use the product rule to find the derivative.
For \( h(x) = (2x + 1)^5 \), apply the chain rule.
Learn the essential rules for finding derivatives quickly and efficiently.